Oswald is dead. Getting rare or not by that time we are talking about assassinating the First Lady in Texas. He would be a dead man walking.
Assuming Oswald isn't killed by Ruby in this scenario, he'll probably be tried by the States of Texas for the murder of Jackie Kennedy in Dallas. The killing of a President-much less a member of his family-wasn't a federal crime in 1963. So, it's the State of Texas or bust, and murder down there, then as now, is a capital crime. And he'll certainly be convicted of same. Whether or not a death sentence will be carried out in that era is another matter. Executions were becoming ever more rare in that period, even in Texas (the last Texas execution in the pre-Furman era was in 1964). So, who knows?
How can I support a man who won't leave politics to take care of his motherless children?
It's possible to think about it both ways.
I don't disagree that there would be great sympathy for Kennedy in public opinion, but much still depends on what actually happens in 1964, who the Republicans nominate, and so on.
I wrote a TL about Oswald going to trail for the two murders. He would certainly still kill Officer Tippit ITTL. I did not think a Dallas judge would give Oswald a plea bargin, unless he or she was retiring. So he would probably get the death penalty. I thought that conspiracy theorists would file enough appeals to drag his case past 1972 and have Fuhrman v Georgia cancel his execution. The death of a First Lady would not inspire nearly as many conspiracy theories. oOswald is more likely to be executed ITTL.